SOLUTION: {{{x^2+6x+8=0 }}} Can you help me solve this please? and Thank you .

Algebra ->  Square-cubic-other-roots -> SOLUTION: {{{x^2+6x+8=0 }}} Can you help me solve this please? and Thank you .      Log On


   

Question 454574: x%5E2%2B6x%2B8=0+
Can you help me solve this please? and Thank you .
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2+%2B+6x+%2B+8+=+0+
First subtract +8+ from both sides
+x%5E2+%2B+6x+=+-8+
Take 1/2 of the coefficient of x,
square it, and add it to both sides
+x%5E2+%2B+6x+%2B+%286%2F2%29%5E2+=+-8+%2B+%286%2F2%29%5E2+
+x%5E2+%2B+6x+%2B+9+=+-8+%2B+9+
+x%5E2+%2B+6x+%2B+9+=+1+
Note that both sides are now perfect squares
and can be written as:
+%28+x+%2B+3+%29%5E2+=+1%5E2+
Take the square root of both sides
+x+%2B+3+=+1+
+x+=+-2+ 1st answer
Note that there is also a negative square root of +1%5E2+
+x+%2B+3+=+-1+
+x+=+-4+ 2nd answer
Now I can check answers by rewriting the answers as:
+x+%2B+2+=+0+
+x+%2B+4+=+0+
These are the factor of the equation, so:
+%28x+%2B+2%29%2A%28+x+%2B+4+%29+=+0+
+x%5E2+%2B+6x+%2B+8+=+0+
OK